In geometry, an icosahedron is a polyhedron that is comprised of twenty faces. In a “regular” icosahedron each of the twenty faces forms an equilateral triangle. The regular icosahedron is one of the five Platonic solids, which have long since been recognized and appreciated by mathematicians for their aesthetic beauty and symmetry. The other four Platonic solids are a regular tetrahedron (pyramid with all faces being equilateral triangles), a regular hexahedron (cube), a regular octahedron (eight-sided figure with all faces being equilateral triangles), and a regular dodecahedron (twelve-sided figure with pentagonal faces).
Applicant's prior U.S. patent application Ser. No. 10/932,403 and U.S. patent application Ser. No. 11/579,307, both of which are incorporated herein by reference, disclose arrays that are comprised of discrete icosahedral elements with interconnecting elements in tension or connection networks along bias directions that interconnect the icosahedral elements.
As discussed in the Applicant's previous applications, polyhedron-based structures, such as icosahedrons, have been recognized to have superior strength-to-weight ratios and other characteristics that make them, at least theoretically, suitable for structural applications. For example, Buckminster Fuller is a well-known geometrist who, among others, pioneered the use of polyhedron-based structures in certain architectural applications, including the geodesic dome.